The present invention relates generally to a self-adaptative control method and a self-adaptative controller implementing said method.
Generally, a controller or regulator is a device operating on one input of a plant for insuring that an output state of said plant is in conformity with a preset fixed or variable value usually called set point. In the field of regulation, "plant" designates a set of active devices comprising actuating means or actuators capable of modifying the characteristics of said devices and parameter sensing means or sensors providing an indication of the state of some parameters. Accordingly, the output of a plant will be the output of a sensor measuring one of the parameters of this plant (or process).
For example, considering an oven which has to be maintained at a constant temperature, the plant will comprise the oven and its content, the heat supply source of the oven, a temperature sensing means for this oven providing an electric signal in correspondence with the temperature and, for example, a servo-valve for regulating a fuel flow aimed to heat the oven. The output of the plant is accordingly the electrical signal indicating the temperature of the oven and input of the plant is an electrical signal capable of controlling the servo-valve.
A conventional control scheme is indicated in the attached FIG. 1. An output value 1 of the plant P (for example the oven temperature signal in the above example) is compared in a comparator 2 with a set point signal 3. The resulting error signal sent to a controller R which provides a control signal at the input of the plant (that is the servo-valve in the above example).
The most common controllers are the controllers called PID (proportional, integral, derivative) which have a transfer function of the following type: ##STR1## In equation (1), the first term between the brackets represents the proportional action, the second one the integral action and the third one the derivative action (p represents the Laplace transform operator). In a simplified way, one can consider that, in the control, the proportional action reduces the stationary error when the gain increases, and increases also the rapidity of the control. However, if the gain increases too much, this can cause oscillations. Accordingly, the integral action is included to eliminate the stationary error and increases the control rapidity. The derivative action, due to its anticipation action (phase advance) provides a stabilization effect.
Therefore, it is necessary to adjust the parameters A, B, C of equation (1) for providing an optimum regulation. However, in practice, two difficulties are encountered. First, the various adjustments are generally not independent and in particular the adjustments of the integral and derivative actions are generally correlated. Second, the derivative action, requires the filtering out of noise which decreases the efficiency of the derivative action.
Additionally, an operator wishing to adjust the control loop for obtaining an optimum operation, for example by minimizing the response time and/or by limiting the overshoot, must adjust three parameters, (the above parameters A, B and C), which are not directly associated with the parameters to be optimized, that is the response time and the overshoot.
Accordingly, in practice where the transfer function of the plant is unknown, the controller is adjusted by successive approximations until satisfactory adjustment is obtained. However, nothing provides any indication to the operator that the obtained control is, in fact, optimized. In practice, due to the complex relationship between the adjustment of the derivative action and the adjustment of the integral action, the operator generally neglects to use the derivative action. It is accordingly clear that, in the greatest number of the practical cases, the optimum control is far from being attained.
Another important practical problem is that the transfer function of the plant varies in time due to various disturbances. For example, in case of the above example, if the fuel pressure towards the electrovalve varies, the action with respect to this electrovalve will have to vary if a good regulation is to be maintained, that is the various controller parameters will have to be varied during the operation. For example, if we consider that the above oven is a polymerization reactor, during the polymerization reaction, the process which is initially endothermic becomes exothermic. It is accordingly clear that, during the operation, the controller characteristics will have to be modified because the transfer function of the plant changes.
For solving this problem, self-adaptative controllers have been designed in the art.
An adaptative control system is essentially a feedback system which automatically provides a desired response in the presence of important external disturbances and large variations of the controlled system parameters. Usually, this system comprises various devices, some of which measure the dynamic parameters of the control system and others modify the characteristics of the control element in accordance with a comparison of the measurements in order to optimize the "cost" function. In greater detail, an adaptative control system results from three considerations:
(1) definition of a prima facie optimum behaviour, from a cost function or performance index of a prima facie optimum behaviour; PA1 (2) continuous comparison between the desired performances and the obtained performances; and PA1 (3) adjustment of the control system parameters in order to minimize the existing gap measured in the above point 2. PA1 (1) the controller R must always include differentiators for providing derivative actuating signals of the first, second, third . . . order according to the nature of the process. As noted above, the such differentiators entail associated filtering problems. PA1 (2) FIG. 2 shows that the regulation is satisfactory when the set point signal 3 is variable. However, when the set point signal is constant, the reference model is reduced to a stationary gain and the adaptation of the controller is no long produced even if disturbances are present.
Accordingly, an optimum control system is considered to be an adaptative system in which the performance index is directly measured. Although it is difficult to classify adaptative systems into general classes, one can categorize the systems utilizing : a reference model; the pulse response from test signals or correlation, the optimum control; and various approaches using a digital computer. We shall consider here only the adaptative systems with a reference model which are particularly flexible and exhibit a great number of practical advantages.
An example of model-reference self-adaptative controller according to the prior art is shown in FIG. 2. In this figure, the same reference depict the same elements as in FIG. 1, that is a plant output signal 1, a comparator 2, a set point signal 3, a controller R and a plant P. A reference model 10 also receives the set point signal 3, and the output 11 of this reference model is compared with the output 1 of the plant. The resulting error signal e is applied to the controller R through an adaptation mechanism 12. The adaptation mechanism 12 cooperates with the controller R in order that the unit comprising the controller and the plant has the same transfer function as the model 10, said function being predetermined.
A great number of theories deal with adaptative control mechanism and one can cite, for example, the Whitaker's method commonly called "MIT synthesis rule" which consists in minimizing the integral of the square of the error e between the model and the plant; the second Liapounov method; and methods implementing the hyperstability theory such as the Landau's method.
All those methods, providing adaptation algorithms, are cited here only for indicating that it is known in the art to adapt a controller for modifying its transfer function and adapt same to the variation of the transfer function of a plant due to structural disturbances.
Referring again to the prior art scheme shown in FIG. 2, it should be noted, however, that despite the improvement provided by the reference model and the self-adaptation of the regulator, important drawbacks remain. One can particularly cite the following points: